Final answer:
The color change of an indicator occurs over a range of pH values. The approximate pH at which the color change becomes visible for an indicator with a pKa of 9.00 is around 8.00.
Step-by-step explanation:
The color change of an indicator is not abrupt but occurs over a range of pH values. The ratio of [In-] to [HIn] changes from 0.1 at a pH one unit below the pKa to 10 at a pH one unit above the pKa. Most indicators change color over a pH range of about two units.
Since the pKa of the indicator in question is 9.00, the color change will be visible when the pH is one unit above or below the pKa. Therefore, the approximate pH at which the color change becomes visible is around 8.00.